It's definitely possible, but is hard to do well unless you take a research block(s). At my school, we could take up to 3 months of research elective time during 3rd year. I think most people ended up doing at least 1 month. It can also serve as a nice break/change of pace from clerkships.
I do know people who worked on research 'on the side', particularly during lighter/outpatient rotations. So it's possible, but difficult to do well because you're still working a lot and have to study during the clerkship. Would not recommend during tough clerkships like medicine or surgery.